Well, there are clearly many possible answers to this excellent question. I will respond by just focussing on one alone, which is the Gothic idea of the double or the doppelganger. Running throughout this excellent Victorian Gothic novel is the idea that we have another "self" and the way that this "self" is actually a much more frightening manifestation of us than we allow to appear in our normal lives. In Gothic literature, this idea of the double is terrifying on the one hand, in terms of the way that it questions the uniqueness of identity, but at the same time it is also alien, as we project into our other selves aspects of our psyche that we repress or ignore.
Of course, the doppelganger in this novel is the painting of Dorian, that he describes as a mirror to his soul. Significantly, after the death of Sybil Vane and his acceptance of its power to reveal his own inner corruption whilst preserving his youthful beauty, he says:
Eternal youth, infinite passion, pleasures subtle and secret, wild joys and wilder sins--he was to have all these things. The portrait was to bear the burden of his shame; that was all.
The relationship between Dorian and his portrait is thus established, and through the Faustian pact that Dorian makes, he is able to preserve his beauty and innocence overtly whilst being free to indulge in all of his most corrupted vices. Thus Dorian splits his soul and body in a way that will have unforeseen consequences for himself, as the end of the story indicates.